Mathematics Faculty Articles
Document Type
Article
Publication Date
7-25-2012
Publication Title
Advances in Numerical Analysis
ISSN
1687-9562
Volume
2012
Issue/No.
2012
First Page
32pp
Abstract
We present a general theory for regularization models of the Navier-Stokes equations based on the Leray deconvolution model with a general deconvolution operator designed to fit a few important key properties. We provide examples of this type of operator, such as the (modified) Tikhonov-Lavrentiev and (modified) Iterated Tikhonov-Lavrentiev operators, and study their mathematical properties. An existence theory is derived for the family of models and a rigorous convergence theory is derived for the resulting algorithms. Our theoretical results are supported by numerical testing with the Taylor-Green vortex problem, presented for the special operator cases mentioned above.
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
NSUWorks Citation
Stanculescu, Iuliana; Ingram, R.; Mays, N; and Manica, C. C., "Convergence Analysis of a Fully Discrete Family of Iterated Deconvolution Methods for Turbulence Modeling with Time Relaxation" (2012). Mathematics Faculty Articles. 115.
https://nsuworks.nova.edu/math_facarticles/115
DOI
10.1155/2012/162539
Comments
Copyright © 2012 R. Ingram et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.